Scouts can be killed by conventional weapons, but AX are more effective. So I converted my FGS to a dedicated Scout killer (I have several other ships to go for the big ones, Gauss is the way to go there) to defend Deneb Algedi. After much experimenting, I run 1x large AX mc turret and 3x medium AX mc turrets now, rest conventional multicannons with OC. Plus an SLF bay with AX Taipans - the fighter pilot doesn't make too many kills on her own, but distracts some of the Scouts during the initial stage where 8 or more fire at you simultaneously. Initially, I also had Gauss cannons fitted, but dropped them, for the Scouts are rather nimble while the FGS is not and fixed weaponry did not work too well for me, in particular with railguns which don't fire instantly. AX turrets are simply more effective (unfortunately, no gimbals available). I would recommend max armour with deep plating and yes, shields are important. I fitted reinforced bi-weaves and those work ok. It's a matter of experimenting, after all. Killed 300+ Scouts last week and about 50 in Capricorni in this one, less than 20 secs per kill.
As has already been said, the worst threat with Scouts is their caustic damage, they can shoot nasty missiles which they seem to do RNG-based and which the FGS cannot reliably evade, and ofc never steer into their death clouds. Turrets have the additional benefit of helping to keep away from them if they are below 10% or so, the FGS can be a little unwieldy. Heat sinks are useful to burn the acid away after a fight, this damages modules, but sometimes is your only choice to get rid of the constant decay otherwise. It should be enough to enable silent running and boosting for some time (DD5).
O7,
[noob]